What is (\partial)/(\partial y)(sin(xy^2z^3)) ?

The answer to (\partial)/(\partial y)(sin(xy^2z^3)) is cos(xy^2z^3)*2xz^3y

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(\partial)/(\partial y)(sin(xy^2z^3))

\frac{\partial}{\partial y} (sin (x y^{2} z^{3}))

cos (x y^{2} z^{3}) \cdot 2 x z^{3} y

Solution steps

\frac{\partial}{\partial y} (sin (x y^{2} z^{3}))

Treat

x, z

as constants

Apply the chain rule:

cos (x y^{2} z^{3}) \frac{\partial}{\partial y} (x y^{2} z^{3})

= cos (x y^{2} z^{3}) \frac{\partial}{\partial y} (x y^{2} z^{3})

\frac{\partial}{\partial y} (x y^{2} z^{3}) = 2 x z^{3} y

= cos (x y^{2} z^{3}) \cdot 2 x z^{3} y

\frac{\partial}{\partial x} (6 y^{2} + 284 x - 12)

\frac{d}{d x} (\frac{- 2 x}{( 1 + x ^{2} ) ^{2}})

y = e^{7}

y^{^{''}} - 6 y^{^{'}} + 4 y = 0, y (0) = 0, y^{^{'}} (0) = 7

e^{y} (1 + x^{2}) d y - 2 x (1 + e^{y}) d x = 0

What is (\partial)/(\partial y)(sin(xy^2z^3)) ?
The answer to (\partial)/(\partial y)(sin(xy^2z^3)) is cos(xy^2z^3)*2xz^3y